T(7,3) - Revision history

ScottKnotPageRobot at 15:38, 31 August 2005

2005-08-31T15:38:13Z

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 {{Torus Knot Page|
 m = 7 |

ScottKnotPageRobot at 16:16, 30 August 2005

2005-08-30T16:16:03Z

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ScottTestRobot at 00:46, 29 August 2005

2005-08-29T00:46:01Z

← Older revision		Revision as of 20:46, 28 August 2005
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			<!-- This knot page was produced from [[Torus Knots Splice Template]] -->

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		⚫	{{Torus Knot Page Header\|m=7\|n=3\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html}}
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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
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	<td width=14.2857%><table cellpadding=0 cellspacing=0>		<td width=14.2857%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>13</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>13</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	<tr align=center><td>11</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>11</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[TorusKnot[7, 3]][t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[TorusKnot[7, 3]][t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -6 -5 -3 -2 2 3 5 6		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -6 -5 -3 -2
	1 + t - t + t - t - ~~t + t - t + t</nowiki></pre></td></tr>~~		1 + Alternating - Alternating + Alternating - Alternating -

			2 3 5 6
			Alternating + Alternating - Alternating + Alternating</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[TorusKnot[7, 3]][z]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[TorusKnot[7, 3]][z]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 56}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 56}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[TorusKnot[7, 3]][q, t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[TorusKnot[7, 3]][q, t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 11 13 15 2 19 3 17 4 19 4 21 5 23 5		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 11 13 2 15 4 17 3 19
	q + q + q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t +		q + q + Alternating q + Alternating q + Alternating q +

			4 19 5 21 6 21
			Alternating q + Alternating q + Alternating q +

			5 23 8 23 7 25
			Alternating q + Alternating q + Alternating q +

	21 6 25 7 23 8 25 8 27 9 29 9		8 25 9 27 9 29
	q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t</nowiki></pre></td></tr>		Alternating q + Alternating q + Alternating q</nowiki></pre></td></tr>
	</table>		</table>

	{{Category:Knot Page}}		[[Category:Knot Page]]

ScottTestRobot at 23:43, 28 August 2005

2005-08-28T23:43:29Z

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-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=7|n=3|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html}}
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 {{Knot Presentations}}
 {{Polynomial Invariants}}
 {{Vassiliev Invariants}}
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   q   t  + q   t  + q   t  + q   t  + q   t  + q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:24, 28 August 2005

2005-08-28T01:24:25Z

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DrorsRobot at 02:46, 27 August 2005

2005-08-27T02:46:07Z

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DrorsRobot at 23:35, 26 August 2005

2005-08-26T23:35:28Z

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DrorsRobot at 23:33, 26 August 2005

2005-08-26T23:33:19Z

← Older revision		Revision as of 19:33, 26 August 2005
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	<!-- ~~ailedmath . uwo . c~~$Failedv$~~ildg~~ at [h$Failedn.matuwo . ca		<!-- $Failed$Failedv$ileddge] at [h$Failedn.matuwo . ca
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	c$Faidml K$FaidaFaedsKiledpaaidtort$edailedts$Failedams$Faileding-l$Failed$Failed62</sub>
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			===[[Finite Type (Vassiliev)nvaanFailed===$Failed'''
	\|style="padding-left: 1em;"$Failed)		\|style="padding-left: 1em;"$Failed)
	\|}		\|}

	[[KhovHomolo$Failedeffi oven$Failed> are shoFaile</math>, over ~~ternation < math</math~~>). e ~~sques~~ ~~with~~ <~~f$FailedYe2~~</math>, where <math>s=</th > 2 the ~~signHLRed~~$~~Failedrder~~=1>		[[KhovHomolo$Failedeffi oven$Failed> are shoFaile</math>, over ternationmathmath>). The squares th < failedYe2</math>, where <math>s=</math>22 signHLRed$Fail the<center><$Failedn=center>
		⚫	<td wid$Failedled$Failed>j</td><td> </td$Failed/tr>
	<tr align=center>
			</tab$Failed/$Failedlednter><td>9</td>$Failed><t$Failedo$Failedo$Fail$Failediled>$Failed&$Failedd$Failed>$Faed > $Fa$Fled style="color: red; borpadding:0"><< KnotTheory$Failed
⚫	<td wid$Failedled~~$Fai~~$Failed$Failed/tr>
		⚫	</tr>$$Failed9$Failedd$Failed<$Failed;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Faile$Failailed > --(--(-$Failed------)) tdtd><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$Failedd,$Faileds$Failedi$Failed<$Failedo$Failede$Failedk$Failedi$Failedp$Failedde[-2, 3, -1, 2, -3, 1]</nowiki></pre></td><Failedolor:bl$Faidn[5]:=</nowiki></$Faedrd$Faido$Failed>$Failedea$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$Failednbsp ((($Failed & ) nbsp; ) & )/now$Faile t
	</table></td>
			-$Failed+ borde $Failed < $Fa
	<td wi$F$Failedtd>9</td><td> </td><td>&nbsp$Failedtd bgcolor=yellow>1</$Fl$Faileddd$Failed>$Failed>$Fa$Failed style="color: red; borpadding:0">&$FailedTheory$Failed
		⚫	$Failededo$Failed<$Failede$Failed $Failedd$Failed>$Failede$Failed $Failede$Failed 0px; padd$Failedpre></td><t$Failedadding: 0em"><now$Failed=$Failed/$Faileda$Failede$Failedm$Failed&$Failedr$Failed<$Failed>$Failed<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]=   </nowiki></pre></td><td><p$Failedding: 0em"><nowik$Failed/$Failed>$Failedepadding:0<$Failed<$Failed:$Failedi$Failed"pai$Failed;$Failedi$Failed>$Fapaddg: 0em"><nowiki>S$Faileds$Failedq$Failed<$Failedl$Failedr$Failedk$Failedl$Failedi$Failedt$Failedp$Failedt$Failedi$FailedK$Failedt$Failedorder: 0px; padding: 0em"><nowiki>Out[12]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 12 14
	</tr>$Failed="border: 0$Failed$Failed;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Faile$Failed
	ailed > -----$Failed------
⚫	~~td$Failed~~; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$Failedd,$Faileds$Failedi$Failed<$Failedo$Failede$Failedk$Failedi$Failedp$Failedde[-2, 3, -1, 2, -3, 1]</nowiki></pre></td></$Failedolor: bl$~~$Failed~~/$~~Failedrd~~$~~Failedo~~$~~Faed~~ > $~~Failea~~$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$~~Failed:~~ $Failed &~~nbsp;<~~/now$~~Failed=borde~~ ~~$Failed~~ - t
	-($Failediled < $Fai
⚫	$Failed$~~Failedailedd~~$Failed>$Failede$Failed $Failede$Failed 0px; ~~padding: 0em"><nowiki>In[8]:=</nowiki></pre~~></td><t$Failedadding: 0$~~Failedlede~~$Failedm$Failed&$Failedr$Failed<$Failed>$Failed<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]=   </nowiki></pre></td><td><~~pre~~ ~~style=~~"~~color: $Failedi~~>~~{3, 2}~~</~~nowiki~~>$~~Failedo$Failedrpaddin~~ $Failed/$Failed:$~~Failede~~$~~Failedt$Failedd~~$Failed>$~~Failedd$Failedt$Failedcpadding0~~$Failed~~"8ding~~: 0em"><nowiki>~~Select[AllK~~$~~Failed1/q) === Jones[#]~~$~~Failedr$Failedp~~$Failed~~:$Failedo$Failed>~~$Failedl$~~Failedn~~$Failedl$~~Failede~~$~~Failede~~$~~Failedr~~$~~Failedd~~$~~Failedl~~$~~Failed1~~$~~Failedi~~></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 12 14
	q + q + 2 q + q - q - q</nowiki></pre></td></tr>		q + q + 2 q + q - q - q</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[TorusKnot[3, 2]][a, z]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[TorusKnot[3, 2]][a, z]</nowiki></pre></td></tr>
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 2 9 3		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 2 9 3
	q + q + q t + q t</nowiki></pre></td></tr>		q + q + q t + q t</nowiki></pre></td></tr>
	</table~~></math~~>		</table>

DrorsRobot at 23:28, 26 August 2005

2005-08-26T23:28:41Z

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DrorsRobot at 01:58, 26 August 2005

2005-08-26T01:58:45Z

← Older revision		Revision as of 21:58, 25 August 2005
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	<!-- ~~TorusKnot[7, 3]~~ -->		<!-- -->

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	Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html T(7,3)'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!		Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html T(7,3)'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!

	Visit [http://www.math.toronto.edu/~drorbn/KAtlas/~~Knots~~/7.5.html 7~~<sub>5</sub>~~'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]!		Visit [http://www.math.toronto.edu/~drorbn/KAtlas/TorusKnots/7.3.html T(7,3)'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]!

	{{Knot Presentations\|name=7_5}}		{{Knot Presentations\|name=7_5}}